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Multiscale convergence and reiterated homogenisation

  • G. Allaire (a1) and M. Briane (a2) (a3)
Abstract

This paper generalises the notion of two-scale convergence to the case of multiple separated scales of periodic oscillations. It allows us to introduce a multi-scale convergence method for the reiterated homogenisation of partial differential equations with oscillating coefficients. This new method is applied to a model problem with a finite or infinite number of microscopic scales, namely the homogenisation of the heat equation in a composite material. Finally, it is generalised to handle the homogenisation of the Neumann problem in a perforated domain.

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5 N. Bakhvalov and G. Panascnko . Homogenization: Averaging Processes in Periodic Media, Mathematics and Its Applications 36 (Dordrecht: Kluwer, 1989).

16 G. Dal Maso . An Introduction to Gamma-convergence (Boston: Birkhauser, 1993).

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
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